Specification Procedure For Symmetric Smooth Transition Autoregressive Models

Abstract

Abstract: In this paper, we assess the first-rate specification accuracy of Escribano-Jorda procedure (EJP) over Terasvirta procedure (TP) in the selection of true symmetric STAR model of the financial time series. Daily nonstationary BETAGLASS stock index (BSI) totaling 2472 observations were obtained from Nigerian Exchange Limited for empirical illustrations. Terasvirta sequential tests and Escribano-Jorda tests were carried out; first-order logistic function classified as asymmetric transition function and exponential function classified as symmetric transition function were specified by TP and EJP, respectively.  Both symmetric and asymmetric STAR models were justifiably fitted to percentage BETAGLASS stock returns (PBSR) and the best model was determined at the evaluation stage. The empirical assessment of the fits of both symmetric STAR models and asymmetric STAR models revealed that symmetric STAR models outperformed asymmetric STAR models under consideration. Hence, EJP has greater specification power over TP particularly when the true model of the financial time series is any symmetric STAR model. Owing to the presence of autoregressive conditional heteroscedastic (ARCH) effects, STAR-generalized ARCH (STAR-GARCH) models and autoregressive-GARCH (AR-GARCH) models were specified and fitted to PBSR. On balance, the SPLSTAR-GARCH (1, 1) model with generalized hyperbolic skew-student’s t innovations outperformed the competing models. Also, the overall prediction performance of the SPLSTAR-GARCH (1 1) model is better than its linear counterpart based on the Akaike information criterion and forecast root mean square error.